Line p passes through (8, -6) and is perpendicular to the line 2x + y = -7.

the slope of line p is .
the equation of line p is y = 1/2x +

y = (1/2)x - 10

Step-by-step explanation:

First we determine the slope of new line p.  This slope is the negative reciprocal of the given line 2x + y = -7.  Solving 2x + y = -7 for y is the easiest way in which to determine the slope of this line.  y = -2x - 7 has the slope -2.

The negative reciprocal of this slope -2 is +1/2.

Given that line p passes through (8, -6) and that the slope of p is 1/2, we can easily solve for the y-intercept, b, of p:

Starting with y = mx + b, we get -6 = (1/2)(8) + b, or -6 = 4 + b.  

Then b = -10, and the equation of line p is y = (1/2)x - 10.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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step-by-step explanation: